I suspect that most implementations of Common Lisp just call the C standard library catan(3) etc, which are well tuned. $ clisp Welcome to GNU CLISP 2.49.92 (2018-02-18) http://clisp.org/ [1]> (atan #c(0 1d-40)) #C(0 1.0d-40) In this particular case, the problem is that the Haskell Data.Complex code has its own implementation of atan, which uses a log(1 + x) in calculating the imaginary part. A foreign function call to the appropriate libm routine would robustly address this, but that would be difficult because it's trying to be generic over RealFloat a => Complex a, instead of special casing Complex Float / Complex Double. Anyway, the Standard Prelude code for this is naïve: it should call log1p, at the very least—which it actually goes to the trouble of defining correctly, but not exporting.